Verification of the possibility to use the variational method for estimating nuclear concentration uncertainties in a burnup problem

Since the 1990s, various fuel burnup calculation systems have been developed that combine the program code for solving the neutron transport equation and the program code for burnup. These numerical methods are acceptable for calculating the isotopic composition of the fuel. However, to ensure the reliability of the results, it is currently necessary that the results of reactor calculations using program codes be accompanied by an assessment of all error components, since this directly affects the efficiency, economy and safety of the designed reactor plant. At present, much attention is paid to assessing the impact of uncertainties in nuclear data on the parameters of various reactor facilities. However, the influence of uncertainties in nuclear data on the main parameters (k_eff, reaction rates, etc.) is mainly studied using sensitivity coefficients. The transfer of errors in the input parameters of the fuel burnup problem (neutron flux density, reaction rates, etc.) to the nuclear concentrations obtained in the course of calculations was studied in a number of works. In the proposed work, for a model problem that makes it possible to obtain an analytical solution to the problem of fuel burnup, comparative calculations of nuclear concentrations and their errors, due to the error in the neutron flux density and capture reaction cross sections for ²⁴⁰Pu, were carried out using the analytical approach and the variational method (1% sensitivity method). There is excellent agreement between the results obtained with both methods. Also, the dependence of the error of nuclear concentrations on the number of burnup steps was studied in the work.